The Fractional Fourier Transform and Applications
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- Publication date
- 1990-03-09
- Usage
- Public Domain


- Topics
- STIRLING ENGINES, THERMAL CONDUCTIVITY, FIBER STRENGTH, REGENERATORS, CARBON FIBERS, COMPOSITE MATERIALS, PERFORMANCE TESTS, DESIGN ANALYSIS, FLOW VELOCITY, INFILTRATION, VAPORS
- Collection
- nasa_techdocs
- Contributor
- NASA
- Language
- English
- Rights
- Public Domain
- Item Size
- 5.2M
The paper describes the 'fractional Fourier transform', which admits computation by an algorithm that has complexity proportional to the fast Fourier transform algorithm. Whereas the Discrete Fourier Transform (DFT) is based on integral roots of unity e(sup (-2(pi)i)/n), the fractional Fourier transform is based on fractional roots of unity e(sup -2(pi)i(alpha)) , where alpha is arbitrary. The fractional Fourier transform and the corresponding fast algorithm are useful for such applications as computing DFTs of sequences with prime lengths, computing DFTs of sparse sequences, analyzing sequences with non-integer periodicities, performing high-resolution trigonometric interpolation, and detecting signals with linearly drifting frequencies. In many cases, the resulting algorithms are faster by arbitrarily large factors than conventional techniques.
- Accession-id
- 97N71297
- Addeddate
- 2011-05-23 05:58:03
- Document-source
- CASI
- Documentid
- 19970015100
- Identifier
- nasa_techdoc_19970015100
- Identifier-ark
- ark:/13960/t9g45kc58
- Nasa-center
- Ames Research Center
- Ocr
- ABBYY FineReader 8.0
- Online-source
- http://wayback.archive-it.org/1792/20100130233544/http://hdl.handle.net/2060/19970015100
- Original-nasa-rights
- Unclassified; No Copyright; Unlimited; Publicly available; Final Report
- Ppi
- 400
- Report-number
- E-10646; NAS 1.26:202322; NASA-CR-202322
- Updated-added-to-ntrs
- 2009-10-09
- Year
- 1990
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